Last year’s stock-market surge boosted 401(k) accounts, but millions of Americans are still likely to run short of money in retirement, according to a pair of studies released Thursday.

The average 401(k) balance reached a new record of $89,300 in the fourth quarter, up 15.5% from a year earlier, according to mutual-fund giant Fidelity Investments. More than three-quarters of the gain came from rising stock prices.

The rising market helped the average 401(k) balance nearly double from a bear-market trough of $46,200 in March 2009, according to Fidelity.

However, Americans' overall retirement prospects improved only fractionally last year, considering all the factors that affect long-term financial health, according to an analysis by the nonpartisan Employee Benefit Research Institute.

The percentage of so-called early baby boomers who will probably not run out of money in retirement improved to 56.7% at year-end, according to EBRI. That was up only a tad from 55.1% at the end of 2012.

That implies, of course, that 43.3% of early boomers probably will run out of money in their later years.

Early boomers are generally thought of as people in their late 50s or 60s who are in or near retirement age.